Abstract
On the basis of the joint tree model initiated in Liu (The non-orientable maximum genus of a graph (in Chinese), Scieulia Sinica, Special Issue on Math. I 191–201, 1979) and comprehensively described in Liu (Theory of Polyhedra (in English), Science Press, Beijing, 2008), this paper provides the numbers of topologically non-equivalent orientable embeddings of a new type of 3-regular graphs by genus via classifying the associate polyhegons.
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